The present invention is in the field of electromagnetic media and devices.
The behavior of electromagnetic radiation is altered when it interacts with charged particles. Whether these charged particles are free, as in plasmas, nearly free, as in conducting media, or restricted, as in insulating or semiconducting mediaxe2x80x94the interaction between an electromagnetic field and charged particles will result in a change in one or more of the properties of the electromagnetic radiation. Because of this interaction, media and devices can be produced that generate, detect, amplify, transmit, reflect, steer, or otherwise control electromagnetic radiation for specific purposes. In addition to interacting with charges, electromagnetic waves can also interact with the electron spin and/or nuclear spin magnetic moments. This interaction can be used to make devices that will control electromagnetic radiation. The properties of such media and devices may further be changed or modulated by externally applied static or time-dependent electric and/or magnetic fields. Other ways of producing changes in a medium or device include varying temperature or applied pressure, or allowing interactions with acoustic, ultrasonic, or additional electromagnetic waves (from low frequencies up through the optical). Other changes could be effected by introducing charged particle beams into the device or medium.
When electromagnetic radiation is incident on a medium composed of a collection of either homogenous or heterogeneous scattering entities, the medium is said to respond to the radiation, producing responding fields and currents. The nature of this response at a given set of external or internal variables, e.g., temperature and pressure, is determined by the composition, morphology and geometry of the medium. The response may, in general, be quite complicated. However, when the dimensions and spacing of the individual scattering elements composing the medium are less than the wavelength of the incident radiation, the responding fields and currents can be replaced by macroscopic averages, and the medium treated as if continuous.
The result of this averaging process is to introduce averaged field quantities for the electric and magnetic fields (E and B, respectively), as well as the two additional averaged field quantities H and D. The four field vector quantities are related at each frequency xcfx89 by the relations B=xcexc(xcfx89)H and D=xcex5(xcfx89)E, where xcex5(xcfx89) represents the medium parameter known as electrical permittivity, and xcexc(xcfx89) represents the magnetic permeability. Wave propagation within a continuous medium is characterized by the properties of the medium parameters. A continuous medium is one whose electromagnetic properties can be characterized by medium parameters that vary on a scale much larger than the dimension and spacing of the constituent components that comprise the medium. At an interface between a first continuous medium and a second continuous medium, wave propagation is characterized by both the medium parameters of the first continuous medium as well as the medium parameters of the second continuous medium. The medium parameters may have further dependencies, such as on frequency or direction of wave propagation, and may also exhibit nonlinear response. There are limitations on the nature of xcexc(xcfx89) and xcex5(xcfx89) that must be consistent with known physical laws; but many forms, such as tensor representation, can occur in practice.
Naturally occurring media-those media either typically found in nature, or that can be formed by known chemical synthesisxe2x80x94exhibit a broad, but nonetheless limited, range of electromagnetic response. In particular, magnetic effects are generally associated with inherently magnetic media, whose response falls off rapidly at higher frequencies. It is thus difficult to find media with significant permeability at RF and higher frequencies. Furthermore, media that possess the important property of negative permeability are very rare, and have only been observed under laboratory conditions in specialized experiments. In contrast, many metals exhibit a negative permittivity at optical frequencies, but other media exhibiting values of negative permittivity at optical or lower frequencies (GHz, for example) are not readily available.
The averaging process that leads to the determination of medium parameters in naturally occurring media, where the scattering entities are atoms and molecules, can also be applied to composite mediaxe2x80x94media formed by physically combining, mixing, or structuring two or more naturally occurring media, such that the scale of spatial variation from one medium to the next is less than the range of wavelengths of the electromagnetic radiation over which the resulting medium is to be utilized. In many composite media, macroscopic scattering elements replace microscopic atoms and molecules; yet the resulting composite can be considered a continuous medium with respect to electromagnetic radiation, so long as the average dimension and spacing are less than a wavelength.
Nearly all practical naturally occurring and composite media have a permittivity and permeability both greater than zero, and generally equal to or greater than unity, at typical frequencies of interest. Such media are considered transparent if the inherent losses (imaginary parts of the permittivity or permeability) are sufficiently small. In transparent media, electromagnetic fields have the form of propagating electromagnetic waves, although the small amount of damping present may lead to absorption of a portion of the electromagnetic energy. If either the permittivity or the permeability is negative, but not both, then electromagnetic fields are non-propagating, and decay exponentially into the medium; such a medium is said to be opaque to incident radiation provided its thickness is greater than the characteristic exponential decay length. A familiar and pertinent example of a medium that can be either opaque or transparent depending on the frequency of excitation is given by a dilute plasma, which has a frequency dependent permittivity given by                               ϵ          ⁡                      (            ω            )                          =                  1          -                                    ω              p              2                                      ω              2                                                          (        1        )            
where xcfx89p is a parameter dependent on the density, charge, and mass of the charge carrier; this parameter is commonly known as the plasma frequency. For this illustration, xcexc is assumed to be unity for all frequencies. Below the plasma frequency, the permittivity is negative, and electromagnetic waves cannot propagate; the medium is opaque. Above the plasma frequency, the permittivity is positive, and electromagnetic waves can propagate through the medium. A familiar example of a dilute plasma is the earth""s ionosphere, from which low-frequency radiation is reflected (when xcex5(xcfx89) less than 0), but which transmits high-frequency radiation.
A wave propagating in the z-direction through a medium has the form exp[in(xcfx89)xcfx89z/cxe2x88x92ixcfx89t], where i is the square root of xe2x88x921, and n2(xcfx89)=xcex5(xcfx89)xcexc(xcfx89). A plane wave thus oscillates with time and position whenever the product xcex5(xcfx89)xcexc(xcfx89) is positive, and decays exponentially whenever the product xcex5(xcfx89)xcexc(xcfx89) is negative. For transparent media, the product is positive and waves propagate.
Composite or naturally occurring media in which both xcex5(xcfx89)) and xcexc(xcfx89) are simultaneously negative have not been previously known. If both xcex5(xcfx89) and xcexc(xcfx89) are simultaneously negative, the product xcex5(xcfx89)xcexc(xcfx89) is once again positive, and electromagnetic waves propagate. Thus, the square root is a real quantity, raising the question of whether electromagnetic waves can propagate in such a medium. Since only the product xcex5(xcfx89)xcexc(xcfx89) enters into the form of a plane wave, it at first appears that there is no difference between a medium where both xcex5(xcfx89) and xcexc(xcfx89) are simultaneously positive and a medium where both xcex5(xcfx89) and xcexc(xcfx89) are simultaneously negative.
In 1968, Veselago theoretically considered the properties of a medium in which both xcex5(xcfx89) and xcexc(xcfx89) were assumed to be simultaneously negative, by examining the solutions of Maxwell""s equations. Even though Veselago noted that such a medium was nonexistent at the time, he pointed out that the existence of such media was not ruled out by Maxwell""s equations, and presented a theoretical analysis of the manner in which electromagnetic waves would propagate. See, V. G. Veselago, Soviet Physics USPEKHI 10, 509 (1968). Veselago concluded that wave propagation in a medium with simultaneously negative xcex5(xcfx89) and xcexc(xcfx89) would exhibit remarkably different properties than media in which xcex5(xcfx89) and xcexc(xcfx89) are both positive.
In usual media, when both xcex5(xcfx89) and xcexc(xcfx89) are simultaneously positive, the direction of the energy flow, and the direction of the phase velocity (or wavevector k) are in the same direction of Exc3x97H. We term such a medium right-handed. When xcex5(xcfx89) and xcexc(xcfx89) are both negative, the direction of the phase velocity, given by Exc3x97B, is opposite to the direction of energy flow, given by Exc3x97H, as H=B/xcexc. The directions of the field vectors E and H, and the direction of the propagation wavevector k thus form a left-handed coordinate system, and Veselago termed media with simultaneously negative xcex5(xcfx89) and xcexc(xcfx89) left-handed media (LHM). Furthermore, Veselago suggested that the correct index-of-refraction n(xcfx89) to be used in the interpretation of Maxwell""s equations should be taken as the negative square root of the product xcex5(xcfx89)xcexc(xcfx89), and thus that left-handed media could be equivalently referred to as negative refractive index media. The property of negative refractive index holds profound consequences for the optics associated with left-handed media, and Veselago pointed out several examples of how geometrical optics would be altered for lenses and other objects composed of left-handed media. For example, a converging lens made of left-handed medium would actually act as a diverging lens, and a diverging lens made of left-handed medium would actually act as a converging lens. Also, the rays emanating from a point source next to a planar slab of LHM could, given the correct geometry and value of index-of-refraction, be brought to a focus on the other side of the slab.
Veselago predicted a number of electromagnetic phenomena that would occur in a LHM, including reversed refraction, reversal of the Doppler shift and Cerenkov radiation, and the reversal of radiation pressure. These phenomena were not demonstrable by Veselago due to the lack of a physical realization of a left-handed medium.
The invention concerns composite media having simultaneous negative effective permittivity and permeability over a common band of frequencies. A composite medium of the invention combines media, which are either themselves separately composite or continuous media, each having a negative permittivity and a negative permeability over at least one common frequency band. Various forms of separate composite and continuous media may be relied upon in the invention.
In a preferred embodiment, one or both of the negative permeability and negative permittivity media used in the composite medium of the invention may be modulated via stimuli. Additionally, the medium or a portion thereof may contain other media that have medium electromagnetic parameters that can be modulated. The frequency position, bandwidth, and other properties of the left-handed propagation band can then be altered from within or without, for example, by an applied field or other stimulus. This modulation could result, for example, in a composite medium that may be switched between left-handed and right-handed properties, or between transparent (left-handed) and opaque (non-propagating) over at least one band of frequencies. In addition, in a left-handed medium of the invention it may be useful to introduce an intentional defect, e.g., a right handed element or set of elements to act as a scattering xe2x80x9cdefectxe2x80x9d within the medium. More than one defect or arrays of defects may also be introduced.
A preferred composite media includes a periodic array of conducting elements that can behave as a continuous medium for electromagnetic scattering when the wavelength is sufficiently longer than both the element dimension and lattice. The preferred composite medium has an effective permittivity xcex5eff(xcfx89) and an effective permeability xcexceff(xcfx89) which are simultaneously negative over a common band of frequencies.